$${ \left( \frac{ \sqrt{ 3 } }{ 2 } \right) }^{ 2 } =1-2 { \left( \frac{ 1 }{ 2 } \right) }^{ 2 }$$
$\text{false}$
$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}=1-2\times \left(\frac{1}{2}\right)^{2}$$
$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}=1-2\times \frac{1}{4}$$
$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}=1-\frac{1}{2}$$
$$\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}=\frac{1}{2}$$
$$\frac{3}{2^{2}}=\frac{1}{2}$$
$$\frac{3}{4}=\frac{1}{2}$$
$$\frac{3}{4}=\frac{2}{4}$$
$$\text{false}$$
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